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At any time, there are areas of science where we are standing at the frontier of knowledge, and can wonder whether we have reached a fundamental limit to human understanding. What is ultimately possible in physics? I will argue here that it is ultimately impossible to answer this question. For this, I will first distinguish three different reasons why the possibility of progress is doubted and offer examples for these cases. Based on this, one can then identify three reasons for why progress might indeed be impossible, and finally conclude that it is impossible to decide which case we are facing.

Author Bio

Sabine Hossenfelder is a theoretical physicist who works on the phenomenology of quantum gravity and physics beyond the Standard Model. Together with her husband she writes a blog called "Backreaction."

You say, "no proof is ever better than its assumptions." No proof is ever worse than its political support. Euclidean geometry appeared ~270 BC. Lobachevsky 1829, Bolyai 1832; Riemann 1854. Nobody over 2100 years' span inscribed a triangle onto a clay ball and saw contradiction? String theory and SUSY are vast employments bouying Official Truth, and it them.

Physics' observables derive from symmetry breakings, yet fashionable theory arises from mathematical inevitabilities of maximal symmetries. Noether's theorems choke on parity, Yang and Lee rebuffed particle theory, nobody can assign a template for biological homochirality, torque is not the same in a mirror. If the vacuum is fundamentally a left shoe in the massed sector, where does that leave theory derived from assuming it is a sock? (not a tabi sock!).

You say "Scientific progress is driven by curiosity... It lives from creativity, from stubbornness, and from hope." Here's a quote, "No one knows the shape of that future or where it will take us. We know only that it is always born in pain." And one more, "mediocrity is a vice of the doomed." Question authority with empirical observation. Somebody should look.

Doubts, uncertainities, difficulties, impossibilities are all there to be faced in life as in Physics or any other professional field. Optimism, hope, faith and zestful adventure provide the spices for life to live usefully. Thus, i find your essay as full of optimism and hope that things will work out but never perfectly. Sciences are all aiming at better and better relative truths and not truth as such. The latter may be the domain for the religions of the world. In my own essay on this forum, i have indicated some impossibilities, besides given out the successful achievements. It is the individual that may be limited but not the humanity or sciences that have limits to cross always.

I have read your essay and I think that it is possible to answer the question what is ultimately impossible in physics, but the most physicists do not like this position, especially those, whose profession is thinking about the universe.

You have also talked about this internal attitude of modern physicists. You wrote, that they have a love-hate relationship...

I have read your essay and I think that it is possible to answer the question what is ultimately impossible in physics, but the most physicists do not like this position, especially those, whose profession is thinking about the universe.

You have also talked about this internal attitude of modern physicists. You wrote, that they have a love-hate relationship with no-go theorems. They love them for the power to sort out possible options and reduce the space of theories that have to be considered. But they also hate them because a considerable amount of possibilities how they can think about the universe are lost.

Although physicists are hating such no-go theorems, they are still dreaming of a final theory.

But until today they do not really know how such a final theory look like. This ignorance has as conceived by me a reason. Actually physicists do not know what is really the ultimate foundation of our universe.

In metaphysics such a foundation was naturally given. It was the ONE, which was considered as an omnipresent entity which embraced all phenomena without any exception. If we would be able to deal with this entity in a scientific way the question for the ultimate foundation of our universe would be answered. But until today metaphysician did not find a serious way to introduce the ONE into physics, because it was considered of being of transcendent nature, too. It is clear, that such an entity, which is beyond every measure, seems to be a no-go of physics at all.

But there is a way how we can introduce it into physics. The result is actually a single, simple, unifying principle, which is regarded as an integral part of a final theory. I am calling this principle the Principle of Radical-Nonduality. It describes the physical conditions which have to be there in the case of a transcendent, that is, an invisible foundation of the Universe. And just these conditions are including fundamental limits of our understanding. These limits can not be physically crossed, because they lead into something that is literally beyond any physical describability. In short, transcendence is the key to a final theory of modern physics. It is obvious that physicists do not like this conclusion. It goes against their deepest convictions.

It was a good surprise to see your name among the essay submitters. I've read your essay. I must say, it is absolutely topical. You cling to the essay question and your argumentation doesn't stray towards some personal favorite topic. I don't think I succeeded in that for my essay, although I ended up with the same conclusion. "Scientific progress is driven by curiosity, and the desire to contribute a piece to mankind's increasing body of knowledge". That's exactly why one should be concerned with research.

Do you mind if I publish some quotes of your essay on twitter and on my blog, linking to your essay, positively of course?

“Scientific progress is driven by curiosity, and the desire to contribute a piece to mankind’s increasing body of knowledge. It lives from creativity, from stubbornness, and from hope. What I have shown here is that there is always reason to hope.”

-Sabine Hossenfelder-The Frontier of Knowledge

I find your summation to be the most compelling part of your argument, as to why physicists have reason to understand we have not hit the wall with what we can discover about the nature of the world. That is to say, what ultimately could restrict creatures that represent being the manifestation of the conscious nature of the cosmos, whether they are unique to only this world or part of any that is possible; for in the end we have demonstrated as able to contemplate itall. I've always found this to have been best expressed by the late Carl Sagan when he argued the same as follows:

“For we are the local embodiment of a Cosmos grown to self-awareness. We have begun to contemplate our origins; starstuff pondering the stars; organizing assemblages of ten billion billion billion atoms considering the evolution of atoms; tracing the long journey by which, here at least, consciousness arose. Our loyalties are to the species and the planet. We speak for earth. Our obligation to survive is owed not just to ourselves but also to that Cosmos, ancient and vast, from which we sprang.”

thank you for your contribution. I've appreciated your attempt to distinguish the sources of doubt of impossibility in the progress of a particular direction.

I have some problems to quantify the concept of being "a progress possible/impossible in a particular direction" which is the origin of the first part of the contribution. What do you mean by progress? A progress in the experimental techniques? To find the correction to the (n+1)th order in a perturbative calculation? To find a brand new theory which substitute the former? Can progress be defined as such a priori?

I think that a progress in foundational physics can only be defined as the matching between a new scientific theory and an experiment not otherwise explainable with other theories.

Therefore I see a loophole in your reasoning about "practical impossibility" D2 and I2. Is a theory something scientifically acceptable if it can not provide any experimental testable prediction? Can a prediction be something not testable for practical reasons in physics?

My personal answer is that if a model is impossible to be tested in practice, it is not a scientific theory so it is out of the domain of the discussion.

I agree that your conclusion "It's ultimately impossible to answer the question about what is ultimately possibile" is a nice pseudo-Russell antinomy, but I believe that a lack of a rigorous definition of the domain your are considering makes it empty.

I wrote about progress as increasing our understanding of Nature. Yes, of course that includes experimental test, but the essay topic wasn't to explain what physics is. I don't know why you think it is necessary to "quantify" progress. Best,

Hmm. 'Always reason to hope'. Your words inspire me Sabine, as my hope that our capacity to recognise real progress (necessary in other than mathematical terms) has been fading. You have produced a lovely and well organised analysis.

I would be most honoured if you would glance at my own essay, and hope you don't miss the real progress embodied that will answer your questions.

Very timely and topical essay! I agree with your introductory statement that it is ultimately impossible to determine what is ultimately possible in physics. I think your essay then becomes perhaps more about how we can *maximise* our potential to discover all that it *is* possible for us to know, given that your I1) and I2) conditions may ultimately apply.

Very timely and topical essay! I agree with your introductory statement that it is ultimately impossible to determine what is ultimately possible in physics. I think your essay then becomes perhaps more about how we can *maximise* our potential to discover all that it *is* possible for us to know, given that your I1) and I2) conditions may ultimately apply.

You quite rightly and refreshingly raised the issue of the possibly fundamental limit imposed by our brain processes. I believe this is at the core of many of the problems you encapsulate in D3). Our brains can only ever give us a subjective "anthropocentric" perception of the external objective reality that we are trying to understand, even when aided by clever devices like telescopes and Tevatrons. This has often been called the "Prime Reality Interface". It is understandable then that we have evolved mathematics from it's humble beginnings of just being a way to make practical sense of the world for survival, to be our "Platonic" way of modelling that "external" reality. Some have even gone as far as to say reality *is* mathematics (eg Tegmark). Unfortunately, due to some of the resulting D1) no-go theorems, consistency requirements and, I might add, "elegance" requirements, we find ouselves in the situation you describe in D3).

One of the main barriers I see as coming out of all the above relates to time. We consciously sense "duration" and perceive "time" as a continuum in which all change happens. To organise our lives we must then quantify this evolving continuum for which we use clocks and we say that they measure "time". Obviously they only measure change, relative spatial displacements, *not* some abstract background entity we call time. Yet this very same procedure is applied to all of our physical laws, from QM and QFT to GR. What barriers might be removed and what progress might be made if we try to re-formulate our theories only in terms of what we can actually observe, mass/energy in evolving, relational configurations?

It seems there are two main areas of objection to even contemplating this, both of which could be placed under your D1):

1. Occam's Razor - there is nothing to be gained by way of simplification, or in fact a given theory would become more complicated if time is removed or replaced.

To this I would ask, should a theory (eg QM or GR), which is struggling for a consistent physically real interpretation and is known to be incomplete, let alone making any real progress, be persevered with as it is, only because something else may be, at least initially, more difficult? Einstein gave us a much more difficult theory than Newton when he tossed out what was considered to be the "complete explanation" of nature, because he saw that the Newtonian laws were at best incomplete. This resulted in one of the greatest leaps of progress in scientific history!

2. Time (operators, coordinates etc) will always be needed for "ordering" or describing events.

Whilst it has been an indespensible tool in the application of our theories *as they are formulated*, will it ultimately lead to our understanding of reality? Are we being hamstrung by our clocks and our need for quantifying "intervals" of some completely unobservable "continuum" entity? The laws we have now are considered symmetric in "time" (CPT violations may ironically be a symptom of our insistance on "time" as a symmetry?), yet we talk about arrows of time, eg "thermodynamic arrow". Can't thermodynamics be just that, ie entropy, as statistical mechanics, friction, kinematics etc, physical processes that we would still perceive to be "happening" in the usual "forward moving" durational progression we sense, whether they were reversed or even became totally static.

I just think that this "atemporal" way of looking at things may open up ways (for better minds than mine) to maximise our chances of gaining all of the knowledge of reality that we can, at least in principle, possibly comprehend.

By the way, I am not a subscriber to Julian Barbour's "no motion" quantum cosmology model as, for one thing, I don't see how Darwinian laws could operate?!

Anyway, just some thoughts I have had after reading some of the other essays (last years' are very relevant too!)and the various discussion threads. Your essay seemed to provide a nice context to put them in! Many of the authors are describing excellent attempts at this kind of fundamental re-formulation and it is a great credit to the concept and forum provided by FQXi.

A thoughtful and perceptive essay with whose conclusion any reasonable person must concur.

May I suggest there is a fourth category of impossibility, Impossibility through Inertia - the converse of your 3rd category. This can be very applicable to highly talented highly successful communities - too much progress to quickly. Not only is their thinking constrained by their successful methods, their emotional commitments to their established truths prevents them from even contemplating a change of direction.

In retrospect this may be very applicable to physics between 1900 (Planck) and 1975 (Standard Model). Every physicist since then has been thoroughly indoctrinated in the ways of thinking of the success period. It will take a couple of generations of your type 3 "No progress" for new thinking to emerge from within the community.

Pauli recognised this problem. He once said "I am not the person to solve this new problem, I know too much" So did Feynman - see the (first) Feynman quote on E-M theory in the last part of my essay.

it is a bit disheartening to note that the comments made admiringly at your essay have not been able to elicit even a small response from you. Let us learn to value time but we can't ignore the time others spend on attending us for the sack of normal courtesy. Sorry, i am no preacher as i myself have lot of shortcomings that others help me learn about and correct the same hopefully. That is the way science too proceeds!

Sorry, Sabina, yes i now see that you have 3 entries as BEE on your essaay forum, i withdraw my comments of lack of attention.

Now let me seek the reasons for your pessimism about the progress of science being tardy. The reason lie with we scientists who are unable to apply their minds in a fresh, independent manner to the problems at hand and develop biasis towards the existing approaches made that we tend to like for our own sake. What is required is a kind of wide open appraoch that can see the totality of the picture nature presents to us and then see how we can harmonise the apparent variety and discern the underlying unity. Nature is simple but our working minds make it complex!

In a way, i like the philosophy you adopt as it may helps us put more vigour and enthusiasm in our efforts. May be you consider visiting my essay site and oblige me with your wisdom.

since you work on quantum gravity phenomenology it was quite surprising for me to read in your essay that "[to] present day we have no experimental evidence for quantum gravity." What could that possibly mean as we do measure fluctuations in the CMB that may reasonably originate from quantum fluctuations after inflation. These fluctuations are today part of our standard understanding of cosmology in the LCDM model.

I appreciate the direction of this lucid paper but still it's terribly general which makes it seem thinner than perhaps it is. You were nowhere near your word limit; some specificity, a few examples would have been welcome.

"Another example for questioning practical possibility is the emergence of structures on increasingly macroscopic levels. While most particle physicists believe in reductionism and would insist the atomic structures, molecule properties, and chemical reactions can in principle all be derived from the Standard Model of Particle Physics, we are far off achieving such a derivation. Even more glaring gaps arise on higher levels. Can one derive all of biology from fundamental physics? What about psychology? Sociology, anybody? A hardcore believer in reductionism will think it possible."

This is great stuff, and deserves an entire paper of its own, which you could certainly provide. I want it and I'm left feeling frustrated. Maybe if you'd made this paragraph your centerpiece ... anyway, your paper, even as it stands is too good not to be doing at least as well as it is.